Question

Verify the identity.

cot x-pi/2= -tan x

Answer 1

What have you tried on this?

Answer 2

Don't I have to use the 90 degree reflection ?

Answer 3

Sum to product would work nice.

Answer 4

so help me set it up and I'll solve it because I am beyond confused haha.

Answer 5

Is it cot x - pi/2 OR

Cot(x - pi/2) both r quite different

Answer 6

Ah, true.

Answer 7

cot(x-pi/2)=tan x
sorry about that

Answer 8

Yeah

so pi/2 is actually 90 degrees.

U know that cot(90-x) = Tan x ?

Answer 9

ok so I was right about the 90 degree ref. awesome ! haha

Answer 10

haha yeah :P

so if cot(90-x) = Tan x,

Cot(x-90) would mean that x is more than 90 and hence x would be in quadrant 2, where Tan is negative. Hence cot(x-90) = Tan x. (Provided 90 < x < 180)

Answer 11

OR u can say that cot(x-90) = -cot(90-x) = - Tan x

Answer 12

(((((((:
ok I finally understand ok thank you! I just need to stop second guessing myself.

Answer 13

i also need help on this last one : Write the expression as the sine, cosine, or tangent of an angle.

sin 9x cos x - cos 9x sin x

sin 10x

cos 8x

sin 8x

cos 10x

Answer 14

Ah, yes. Even/Odd properties. That would certainly make it quicker!

Answer 15

@luckythebest

Answer 16

Ok.

@mheiges1 do you know that sin(a-b) = sin a cos b - cos a sin b ?

Answer 17

Where do I find the values of A and B to plug in ?

Answer 18

@mheiges1 u don't need to find.

sin 9x cos x - cos 9x sin x is a form of the above identity.

where sin a = sin 9 x and cos b = cos x

hence a = 9x, b = x

so it goes as simple as sin(9x-x) = sin 8x.

Answer 19

sin 8x = sin (9x-x)

sin(9x-x) = sin 9x cos x - cos 9x sin x.

Answer 20

Cot(x-pi/2)=-cot(pi/2-x)=--tanx
because cot(-y)=-Coty [-y is in 4th quadrant & in 4th quadrant cot is negative.

Answer 21

oh ok I gotcha! thanks again dude. you rock @luckythebest

Answer 22

yeah thanks